基于惩罚函数表示的风险度量与g-期望的研究

发布时间：2018-01-21 16:34

本文关键词： 风险度量 g-期望惩罚函数投资组合　出处：《山东大学》2016年硕士论文　论文类型：学位论文

【摘要】：随着全球经济的快速发展,金融市场不断发展和创新,各种金融产品层出不穷,使得金融市场的波动性日益加剧,金融产品蕴含的风险不断增加。风险度量作为风险管理的核心,是金融市场稳步发展的保证。我国金融市场并不完善,面对国内经济的下行压力,如何有效缓解金融风险,形成有效的管理机制,成为当下金融改革的重点。本文主要在惩罚函数和可接受集合的意义下对现有风险度量方法的理论和应用进行系统性的研究。本文首先介绍在可接受集合的意义下风险度量的定义和性质,给出静态情形下凸风险度量、相容风险度量、分布不变的风险度量、熵风险度量、谱风险度量等的定义及对偶表示,重点给出各个风险度量的性质及证明,以此得到各种风险度量之间的关系,然后在动态情形下类似的给出风险度量的定义和表达形式及之间的关系。另外在g-期望意义下,介绍由9-期望诱导的风险度量的性质,并得出在g-概率意义下,由9-期望诱导的风险度量满足分布不变性的充分条件。最后给出风险度量在投资组合上的应用,对均值-熵模型、均值-谱模型进行客观的评价,给投资者提供最优投资组合策略,指导投资者理性投资。
[Abstract]:With the rapid development of the global economy and the continuous development and innovation of the financial market, a variety of financial products emerge in endlessly, which makes the volatility of the financial market increasing day by day. Risk measurement, as the core of risk management, is the guarantee of the steady development of financial market. China's financial market is not perfect, facing the downward pressure of domestic economy. How to effectively mitigate financial risks and form an effective management mechanism. This paper focuses on the theory and application of existing risk measurement methods in the sense of penalty function and acceptable set. First of all, this paper introduces the significance of acceptable set. The definition and nature of risk measurement. The definition and dual representation of convex risk measure, consistent risk measure, distribution-invariant risk measure, entropy risk measure and spectral risk measure are given, and the properties and proofs of each risk measure are given. In this way, the relationship between various risk measures is obtained, and then the definition and expression form of risk measurement and the relationship between them are given in the dynamic situation. In addition, in the sense of g- expectation. The properties of risk measurement induced by 9- expectation are introduced, and the results are obtained in the sense of g- probability. The risk measurement induced by 9- expectation satisfies the sufficient condition of distribution invariance. Finally, the application of risk measurement in portfolio is given, and the mean entropy model and mean spectrum model are evaluated objectively. To provide investors with an optimal portfolio strategy to guide investors to invest rationally.
【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224;F832.5

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